Assignment 5
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School
University of Ottawa *
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Course
2
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
3
Uploaded by MateMosquitoPerson716
ASSIGNMENT 5 •
This assignment is due on Wednesday November 15
th
at 11:59 pm •
This assignment carries a total score of 100 points •
For information regarding penalties, refer to the course outline •
Please submit your solution in handwritten
form. Ensure to scan and convert it into a PDF before uploading it to Brightspace. •
Include a signed statement of academic integrity in your submission •
You are responsible for completing this assignment on your own. The integrity statement prohibits receiving assistance in answering questions through any form of service Statement of Academic Integrity Individual Assignment Checklist & Disclosure Please read the disclosure below following the completion of your assignment. Once you have verified these points, hand in this signed disclosure with your assignment. 1.
I acknowledge to have read and understood my responsibility for maintaining academic integrity, as defined by the University of Ottawa’s policies and regulations
. Furthermore, I understand that any violation of academic integrity may result in strict disciplinary action as outlined in the regulations. 2.
If applicable, I have referenced and/or footnoted all ideas, words, or other intellectual property from other sources used in completing this assignment. 3.
If applicable, a proper bibliography is included, which includes acknowledgement of all sources used to complete this assignment. 4.
This is the first time that I have submitted this assignment or essay (either partially or entirely) for academic evaluation. 5.
I have not utilized unauthorized assistance or aids including but not limited to outsourcing assignment solutions, and unethical use of online services such as artificial intelligence tools and course-sharing websites. Course Code: Assignment No. / Title: Date of Submission:
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1. (25 Points) Monica's boutique had a revenue of $45,000 in its first year, and the revenue has been projected to increase by $2,000 each year. a. Represent the annual percentage growth of the boutique's revenue as a function of time, and illustrate it with a graph. b. Calculate the percentage growth rate of the boutique's revenue after the first year. c. Analyze the long-term behavior of the boutique's annual percentage growth rate. 2. (25 Points) Shortly after launching a new smartphone app, the developer of the app rolled out a targeted social media campaign to increase awareness and downloads. The developer observed that, t days following the launch, P(t) percent of the potential user base had downloaded the app, where a. Determine the rate of change in the download percentage P(t) relative to time after 5 days. Is the download percentage accelerating or decelerating at this point? b. What happens to the rate of change of P(t) as t → +∞
? 3. (25 Points) A distributor of innovative smart home devices predicts that local technology enthusiasts will purchase approximately
2
2
4,374
(
)
4,374
D p
p
p
−
=
=
units of the latest smart thermostat per week when the unit price is p dollars. Additionally, it is projected that 𝑡
weeks from now, the price of the smart thermostat will be 𝑝(𝑡) = 0.02𝑡
2
+ 0.1𝑡 + 6
dollars per unit. a. At what rate is the purchasing trend projected to change with respect to the unit price when the price reaches $9? b. At what rate will the demand for smart thermostat be changing with respect to time 10 weeks from now? Will the purchases be increasing or decreasing at that point? 4. (25 Points) The production quantity Q, of a new pharmaceutical product, quantified in batches, correlates with the amount of research labour, represented by L hours, invested in its development. This relationship is captured by The projection indicates that the allocation of research hours, L, to the project will evolve as the project progresses. The function L(t) details the expected number of research hours at t months from the project's commencement, within the first year (whe
re 0 ≤ t ≤ 12)
a. Calculate the number of research hours that will be invested in the project 5 months from its initiation. How many batches of the product are expected to be developed at that point in time?
b. Determine the rate at which the development output will be changing with respect to time 5 months after the project begins. Will the number of developed batches be rising or falling at this time?
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